I need to develop Leaflet map which will show the whole world. Also, I need to draw some arrows which will show paths of migrations in the world. The important thing to say that those arrows need to be curved. Do you have some advice how can that be shown on the map in Leaflet API?

My ideas:
Is it possible to show some direction arrows with RaphaelJS? I see that Leaflet has Raphael plugin so we can add Raphael object on the map.
Is it possible to draw a polygon which will be arrow shape and overlay it on the map?

Yes a polygon or a line. I would probably go with a line as a polygon will might not look so good at all zoom levels. Whilst a line the thickness will the same at all zoom levels. Do a Google image search for "whether map" you'll probably get some good inspiration there.
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ChrisInCamboDec 19 '12 at 2:07